第二題太簡單,不能作為競賽題。延長QP致外接圓於Q'和P',
由條件可得MKL與AQP相似。得BQ*AQ=AP*PC,又知:QQ'*(QP+PP')=PP'(QP+QQ')得QQ'=PP',由此可知,MQ'=MP',所以M是P'Q'的中點,OM也垂直平分PQ,所以OM=OP,得證.10分鍾不到,搞定.
problem 2 is too easy
本帖於 2009-07-28 16:38:03 時間, 由普通用戶 康MM 編輯
第二題太簡單,不能作為競賽題。延長QP致外接圓於Q'和P',
由條件可得MKL與AQP相似。得BQ*AQ=AP*PC,又知:QQ'*(QP+PP')=PP'(QP+QQ')得QQ'=PP',由此可知,MQ'=MP',所以M是P'Q'的中點,OM也垂直平分PQ,所以OM=OP,得證.10分鍾不到,搞定.
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